On strong basins of attractions for non-convex sparse spike estimation: upper and lower bounds - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Mathematical Imaging and Vision Année : 2023

On strong basins of attractions for non-convex sparse spike estimation: upper and lower bounds

Résumé

In this article, we study the size of strong basins of attractions for the non-convex sparse spike estimation problem. We first extend previous results to obtain a lower bound on the size of sets where gradient descent converges with a linear rate to the minimum of the non-convex objective functional. We then give an upper bound that shows that the dependency of the lower bound with respect to the number of measurements reflects well the true size of basins of attraction for random Gaussian Fourier measurements. These theoretical results are confirmed by experiments.
Fichier principal
Vignette du fichier
sr_optim_necessary.pdf (969.34 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04047677 , version 1 (27-03-2023)

Identifiants

  • HAL Id : hal-04047677 , version 1

Citer

Yann Traonmilin, Jean-François Aujol, Pierre-Jean Bénard, Arthur Leclaire. On strong basins of attractions for non-convex sparse spike estimation: upper and lower bounds. Journal of Mathematical Imaging and Vision, 2023. ⟨hal-04047677⟩

Collections

CNRS IMB INSMI ANR
77 Consultations
66 Téléchargements

Partager

Gmail Facebook X LinkedIn More